0=x^3-5x^2+4x

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Solution for 0=x^3-5x^2+4x equation: 


Simplifying
0 = x3 + -5x2 + 4x

Reorder the terms:
0 = 4x + -5x2 + x3

Solving
0 = 4x + -5x2 + x3

Solving for variable 'x'.
Remove the zero:
-4x + 5x2 + -1x3 = 4x + -5x2 + x3 + -4x + 5x2 + -1x3

Reorder the terms:
-4x + 5x2 + -1x3 = 4x + -4x + -5x2 + 5x2 + x3 + -1x3

Combine like terms: 4x + -4x = 0
-4x + 5x2 + -1x3 = 0 + -5x2 + 5x2 + x3 + -1x3
-4x + 5x2 + -1x3 = -5x2 + 5x2 + x3 + -1x3

Combine like terms: -5x2 + 5x2 = 0
-4x + 5x2 + -1x3 = 0 + x3 + -1x3
-4x + 5x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-4x + 5x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 5x + -1x2) = 0

Factor a trinomial.
x((-4 + x)(1 + -1x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 4, 1}

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